Sample path properties of the local time of multifractional Brownian motion

We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^H=(B^{H(t)}(t),t\in {\mathbb{R}}^{+})$. An analogue of Chung’s law of the iterated logarithm is studied for $B^H$ and used to obtain the pointwise H"{o}lder exponent of the local time. A kind of local asymptotic self-similarity is proved to be satisfied by the local time of $B^H$.